A rack is a right-distributive and right-invertible magma. In other words, the right action of the magma on itself by right translations is automorphic.  (Racks have, therefore, also been called automorphic sets in the literature.)

The IsRack command returns true if the given magma is a rack. It returns false otherwise.

$\mathrm{with}\left(\mathrm{Magma}\right)\:$

$m≔⟨⟨⟨1\left|3\right|2⟩\,⟨3\left|2\right|1⟩\,⟨2\left|1\right|3⟩⟩⟩$

$m≔\left[\begin{array}{ccc}1& 3& 2\\ 3& 2& 1\\ 2& 1& 3\end{array}\right]$

$\mathrm{IsRack}\left(m\right)$

$\mathrm{true}$

$m≔⟨⟨⟨1\left|2\right|3⟩\,⟨2\left|3\right|3⟩\,⟨3\left|1\right|2⟩⟩⟩$

$m≔\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 3\\ 3& 1& 2\end{array}\right]$

$\mathrm{IsRack}\left(m\right)$

$\mathrm{false}$

The Magma[IsRack] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.